A stabilization-free hybrid virtual element formulation for the accurate analysis of 2D elasto-plastic problems

Abstract

A plasticity formulation for the Hybrid Virtual Element Method (HVEM) is presented. The main features include the use of an energy norm for the VE projection, a high-order divergence-free interpolation for stresses and a piecewise constant interpolation for plastic multipliers within element subdomains. The HVEM does not require any stabilization term, unlike classical VEM formulations which are affected by the choice of stabilization parameters. The algorithmic tangent matrix is derived consistently and analytically. A standard strain-driven formulation and a Backward-Euler time integration scheme are adopted. The return mapping process for the stress evaluation is formulated at the element level to preserve the stress interpolation as plasticity evolves. Even though general constitutive laws can be readily considered, to test the robustness of HVEM, an elastic-perfectly plastic behavior is adopted. In such a case, the return mapping process is efficiently solved using a Sequential Quadratic Programming Algorithm. The solution is free from volumetric locking and from spurious hardening effects that are observed in stabilized VEM. The numerical results confirm the accuracy of HVEM for rough meshes and high rate of convergence in recovering the collapse load.